461 - Signatures Review

(worth 15 total)
We want to create a signature for a record file (containing 1 million records) to try and avoid having to search the file for records not found.

The signature is 10K-bits long (10,000 bits)
Each record is run through 4 hash functions to specify 4 bits to set:
int H1 (Record* rec);
int H2 (record* rec).

What kind of data structure do we need for the signature? (an array of 10K elements such as bool Sig[10000] is unacceptable; i.e. the bits need to be packed with no wasted space)

The buffer for the signature is
unsigned char BUF[1250];
Given your signature structure, write the algorithm to set the required bits in the signature for one record. Pseudo-code preferred. Each step must be explained.